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arXiv:1801.08432

BIGSTICK: A flexible configuration-interaction shell-model code (updated)

Calvin W. Johnson, W. E. Ormand, Kenneth McElvain, Zbikowski, Ryan, Shan, Hongzhang

Published Jan 24, 2018• 38 citations
arXivHTMLPDF

Abstract

We present BIGSTICK, a flexible configuration-interaction open-source shell-model code for the many-fermion problem. Written mostly in Fortran 90 with some later extensions, BIGSTICK utilizes a factorized on-the-fly algorithm for computing many-body matrix elements, and has both MPI (distributed memory) and OpenMP (shared memory) parallelization, and can run on platforms ranging from laptops to the largest parallel supercomputers. It uses a flexible yet efficient many-body truncation scheme, and reads input files in multiple formats, allowing one to tackle both phenomenological (major valence shell space) and ab initio (the so-called no-core shell model) calculations. BIGSTICK can generate energy spectra, static and transition one-body densities, and expectation values of scalar operators. Using the built-in Lanczos algorithm one can compute transition probability distributions and decompose wave functions into components defined by group theory. This manual provides a general guide to compiling and running BIGSTICK, which comes with numerous sample input files, as well as some of the basic theory underlying the code. Updated November 2025 to version 8.0.0

DOI
10.48550/arxiv.1801.08432

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We present BIGSTICK, a flexible configuration-interaction open-source shell-model code for the many-fermion problem. Written mostly in Fortran 90 with some later extensions, BIGSTICK utilizes a factorized on-the-fly algorithm for computing many-body matrix elements, and has both MPI (distributed memory) and OpenMP (shared memory) parallelization, and can run on platforms ranging from laptops to the largest parallel supercomputers. It uses a flexible yet efficient many-body truncation scheme, and reads input files in multiple formats, allowing one to tackle both phenomenological (major valence shell space) and ab initio (the so-called no-core shell model) calculations. BIGSTICK can generate energy spectra, static and transition one-body densities, and expectation values of scalar operators. Using the built-in Lanczos algorithm one can compute transition probability distributions and decompose wave functions into components defined by group theory. This manual provides a general guide to compiling and running BIGSTICK, which comes with numerous sample input files, as well as some of the basic theory underlying the code. Updated November 2025 to version 8.0.0
The configuration-interaction shell model is an effective and widely-used approach to the nuclear many-body problem, whose main drawback is the exponential growth of the basis dimension. An useful way to character nuclear shell-model Hamiltonians is through traces, including traces in subspaces defined by orbital occupations. Such traces, or energy centroids, can be easily and efficiently computed through the monopole components of the nuclear interaction, that is, terms that go like nanbn_a n_bna​nb​ where nan_ana​ is the occupation of the single-particle orbital labeled by aaa. These calculations can be carried out very quickly for both empirical (valence space) and no-core shell model spaces and interactions. In fact, they can be carried out so fast, one can use this to optimize an efficient, if approximate, many-body truncation scheme used in available nuclear shell-model codes such as BIGSTICK. To carry out both the traces and the optimization, we present the TRACER code, written in Fortran90 and described and available here. We give example results as well as discuss performance.
CDFCI is a shared-memory parallel numerical program for computing low-lying eigenpairs of large-scale, non-relativistic fermionic Hamiltonians. The software is designed to handle a broad class of many-body quantum models, including both ab initio electronic structure Hamiltonians and lattice-based Hamiltonians arising in condensed matter physics. CDFCI combines an efficient coordinate-descent-based selected configuration interaction algorithm with dedicated parallelization strategies, achieving high performance on modern multi-core architectures. Benchmark results on representative quantum chemistry and condensed matter test cases demonstrate that CDFCI attains state-of-the-art accuracy with competitive performance compared to established selected configuration interaction (such as CIPSI or SHCI) and DMRG implementations. The software is open-source, extensively documented, and provides a Python interface for seamless integration with PySCF and other many-body simulation workflows.
mVMC (many-variable Variational Monte Carlo) is an open-source software package based on the variational Monte Carlo method applicable for a wide range of Hamiltonians for interacting fermion systems. In mVMC, we introduce more than ten thousands variational parameters and simultaneously optimize them by using the stochastic reconfiguration (SR) method. In this paper, we explain basics and user interfaces of mVMC. By using mVMC, users can perform the calculation by preparing only one input file of about ten lines for widely studied quantum lattice models, and can also perform it for general Hamiltonians by preparing several additional input files. We show the benchmark results of mVMC for the Hubbard model, the Heisenberg model, and the Kondo-lattice model. These benchmark results demonstrate that mVMC provides ground-state and low-energy-excited-state wave functions for interacting fermion systems with high accuracy. Program title: mVMC Program Files doi: http://dx.doi.org/10.17632/xhgyp6ncvt.1 Licensing provisions: GNU General Public License version 3 Programming language: C External routines/libraries: MPI, BLAS, LAPACK, Pfapack, ScaLAPACK (optional) Nature of problem: Physical properties (such as the charge/spin structure factors) of strongly correlated electrons at zero temperature. Solution method: Application software based on the variational Monte Carlo method for quantum lattice model such as the Hubbard model, the Heisenberg model and the Kondo model. Unusual features: It is possible to perform the highly-accurate calculations for ground states in a wide range of theoretical Hamiltonians in quantum many-body systems. In addition to the conventional orders such as magnetic and/or charge orders, user can treat the anisotropic superconductivities within the same framework. This flexibility is the main advantage of mVMC.
The exact solution of quantum mechanical many-body problems is only possible for few particles. Therefore, numerical methods were developed in the fields of quantum physics and quantum chemistry for larger particle numbers. Configuration Interaction (CI) methods or the No-Core Shell Model (NCSM) allow ab initio calculations for light and intermediate-mass nuclei, without resorting to phenomenology. An extension of the NCSM is the Importance-Truncated No-Core Shell Model, which uses an a priori selection of the most important basis states. The importance truncation was first developed and applied in quantum chemistry in the 1970s and latter successfully applied to models of light and intermediate mass nuclei. Other numerical methods for calculations for ultra-cold fermionic many-body systems are the Fixed-Node Diffusion Monte Carlo method (FN-DMC) and the stochastic variational approach with Correlated Gaussian basis functions (CG). There are also such method as the Coupled-Cluster method, Green’s Function Monte Carlo (GFMC) method, et cetera, used for calculation of many-body systems. In this thesis, we adopt the IT-NCSM for the calculation of ultra-cold Fermi gases at unitarity. Ultracold gases are dilute, strongly correlated systems, in which the average interparticle distance is much larger than the range of the interaction. Therefore, the detailed radial dependence of the potential is not resolved, and the potential can be replaced by an effective contact interaction. At low energy, s-wave scattering dominates and the interaction can be described by the s-wave scattering length. If the scattering length is small and negative, Cooper-pairs are formed in the Bardeen-Cooper-Schrieffer (BCS) regime. If the scattering length is small and positive, these Cooper-pairs become strongly bound molecules in a Bose-Einstein-Condensate (BEC). In between (for large scattering lengths) is the unitary limit with universal properties. Calculations of the energy spectra (ground-state and first excited-state) have so far only been performed for up to five particles using CI or NCSM methods or for up to six particles using the CG method. Calculations with larger particle numbers have only been performed with Monte Carlo methods and only for the ground state of up to 30 particles. We extend ab initio calculations of the energy spectra of ultra-cold Fermi gases at unitarity for up to 20 particle using the IT-NCSM. For our calculations we use different interactions: an effective interaction introduced by Alhassid, Bertsch and Fang and an interaction constructed using an effective field theory (EFT) approach. Furthermore, we use a Gauss-shaped potential as it is also used for the calculations of ultra-cold Fermi gases at unitarity using CG or FN-DMC methods. Although more effort must be invested to make the Gauss-shaped potential suitable for IT-NCSM calculations of ultra-cold Fermi gases, calculations with the other two interactions yield ground-state energies which agree excellently with the results obtained using the FN-DMC method. The IT-NCSM extends the range of the NCSM and permits the calculation of energy spectra (ground-state and excited-state energies) of fermionic systems with large particle numbers for which previously only the ground states could be calculated using Monte Carlo methods.
The shell model is the standard tool for addressing the canonical nuclear many-body problem of nonrelativistic nucleons interacting through a static potential. We discuss several of the uncontrolled approximations that are made in this model to motivate a different approach, one based on an exact solution of the Bloch-Horowitz equation. We argue that the necessary self-consistent solutions of this equation can be obtained efficiently by a Green's function expansion based on the Lanczos algorithm. The resulting effective theory is carried out for the simplest nuclei, d and 3He, using realistic NN interactions such as the Argonne v18 and Reid93 potentials, in order to contrast the results with the shell model. We discuss the wave function normalization, the evolution of the wave function as the "shell model" space is varied, and the magnetic elastic effective operator. The numerical results show a simple renormalization group behavior that differs from effective field theory treatments of the two- and three-body problems. The likely origin of this scaling is discussed.